 Teacher Support Materials 2008 Maths GCE Paper Reference MM2B Copyright © 2008 AQA and its licensors All rights reserved Permission to reproduce all copyrighted material has been applied for In some cases, efforts to contact copyright holders have been unsuccessful and AQA will be happy to rectify any omissions if notified The Assessment and Qualifications Alliance (AQA) is a company limited by guarantee registered in England and Wales (company number 3644723) and a registered charity (registered charity number 1073334) Registered address: AQA, Devas Street, Manchester M15 6EX Dr Michael Cresswell, Director General MM2B Question Student Response Commentary Most candidates answered this question well; this script shows one of a small proportion of candidates who made an algebraic or arithmetical error in part (c) Mark scheme MM2B Question Student response Commentary This question was answered well by many candidates As in this example, a few lost a mark in part (a) by not showing that the two tensions were different This candidate, in common with a number of others, used incorrect moments in part (b), but “obtained” the given answer by approximating 40g to 21g Most of these then correctly resolved vertically and thus gained marks in part (c); however this candidate used a similar, incorrect moment equation in part (c) and hence scored no marks for this part, and his answer to part (d) was not relevant Mark Scheme MM2B Question Student Response Commentary As in this example, most candidates answered this question well Mark Scheme MM2B Question Student Response MM2B Commentary In general, part (a) was answered well, but again a number of candidates created the answer; if they had obtained 80 000, a factor of 54 clearly was needed to give the printed result This script shows part (a) being answered correctly In part (b), using the formula: Power = Force × Velocity, the candidate calculates the correct force of 4000N exerted by the van’s engine at 25ms–1 Unfortunately, the common error shown here was to forget the resistance force and thus use 4000 = 1500a Mark Scheme Question Student Response Commentary In part (d), v = r and v = 2 , were used in equal numbers As shown in this example, the r values of r and v which candidates substituted were often in vector form, with random attempts made at the division of the two vectors MM2B Mark Scheme Question Student Response MM2B Commentary Virtually all candidates obtained dv = – 0.05v, only a few ignored the required dt dv = –0.05mv dt dv The equation:     0.05 dt was a necessary step which needed to be seen in part (b), as v shown in this example Candidates knew roughly how to obtain v = 20e 0.05t step m Too often, algebraic skills were not sufficient and, as in this script, the equation ln v = – 0.05t + c regularly changed from v = e 0.05t  c , to v = e 0.05t + e c before becoming v =K e 0.05t This and similar errors were not condoned Mark Scheme Question MM2B Student Response Commentary Many candidates made little progress in this question As in this example, a number did not use conservation of energy correctly, with many using the potential energy at B to be zero, and assuming that the kinetic energy at the top was zero These candidates ignored the fact that the bead could not complete full revolutions attached to a string with no speed at the top In part (b), the required components, T and mv , appeared frequently in the equation but r often candidates, including this one, did not find the value of v when the bead was at C Part (c) was usually answered well Mark Scheme Question MM2B Student Response Commentary Part (a) tested that part of the specification, work done = F dx Few candidates found x dx correctly; instead of integrating, a few candidates used the value of the integral to be l x the area under the line y = as shown in this example l  e Unfortunately, many candidates used techniques which were not credited: x for example, elastic potential energy is and x = e; 2l or work done = maximum force × half the distance moved, which is only valid if the force is linear and this was very rarely stated Mark Scheme [...]... = 2 , were used in equal numbers As shown in this example, the r values of r and v which candidates substituted were often in vector form, with random attempts made at the division of the two vectors MM2B Mark Scheme Question 6 Student Response MM2B Commentary Virtually all candidates obtained dv = – 0.05v, only a few ignored the required dt dv = –0.05mv dt dv The equation:     0.05 dt was a necessary... did not find the value of v when the bead was at C Part (c) was usually answered well Mark Scheme Question 8 MM2B Student Response Commentary Part (a) tested that part of the specification, work done = F dx Few candidates found x dx correctly; instead of integrating, a few candidates used the value of the integral to be l x the area under the line y = as shown in this example l  e 0 Unfortunately,... necessary step which needed to be seen in part (b), as v shown in this example Candidates knew roughly how to obtain v = 20e 0.05t step m Too often, algebraic skills were not sufficient and, as in this script, the equation ln v = – 0.05t + c regularly changed from v = e 0.05t  c , to v = e 0.05t + e c before becoming v =K e 0.05t This and similar errors were not condoned Mark Scheme Question 7 MM2B Student... area under the line y = as shown in this example l  e 0 Unfortunately, many candidates used techniques which were not credited: x 2 for example, elastic potential energy is and x = e; 2l or work done = maximum force × half the distance moved, which is only valid if the force is linear and this was very rarely stated Mark Scheme ... candidates made little progress in this question As in this example, a number did not use conservation of energy correctly, with many using the potential energy at B to be zero, and assuming that the kinetic energy at the top was zero These candidates ignored the fact that the bead could not complete full revolutions attached to a string with no speed at the top In part (b), the required components,